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Chain rule/multiple variables

  1. Jun 3, 2014 #1
    1. The problem statement, all variables and given/known data

    Show z(x,y) = cos(xy) is a solution of

    (∂z/∂x)y + (∂z/dy)x = (x+y) ( (∂2z/∂x∂y) + xyz)

    (question also attached if it makes it clearer)

    3. The attempt at a solution

    ∂z= (∂z/∂x)ydx + (∂z/dy)xdy

    ∂z/∂x = -ysin(xy)
    ∂z/∂y = -xsin(xy)

    what does it mean show it is a solution? any tips appreciated
     

    Attached Files:

  2. jcsd
  3. Jun 3, 2014 #2

    CAF123

    User Avatar
    Gold Member

    It means that choice of z(x,y) satisfies the equation. I.e plug in z(x,y) into LHS and into the RHS and they should be equal.
     
  4. Jun 4, 2014 #3
    So for ##z(x,y) = \cos(xy) ##, what is ##\frac{∂^2z}{∂x∂y}##?
     
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